ABSTRACT
Direct numerical simulation (DNS) is widely used as a numerical tool to investigate turbulence. In this chapter, comparisons are made between DNS and CNS results for two-dimensional turbulent Rayleigh-Benard convection. In 2017, Lin, Wang & Liao combined clean numerical simulation (CNS) with the Fourier-Galerkin spectral method (in spectral space) to solve two-dimensional (2D) turbulent Rayleigh-Bénard convection (RBC) for free-slip boundary conditions. Thus, generally speaking, if a turbulent flow has multiple large-scale states, then small disturbances, which are either natural (such as environmental perturbations) or artificial (such as background numerical noise), could lead to random transitions between different states. Background numerical noise from artificial sources is unavoidable when the Navier–Stokes and continuity equations are solved numerically. Likewise, it is also important to know the existence and statistics stability of solutions of the generalized Landau-Lifshitz-Navier-Stokes equation.
